Vermes played his first year in college on the men's soccer team at Loyola College in Maryland under head coach Bill Sento. Vermes then transferred and played three years of college soccer at Rutgers University, from 1985 to 1987, where he elevated the status of the program to that of a national power. In his final season, Vermes scored 21 goals and 10 assists for the team, finishing a first team All-American, as well as runner-up for the National Player of the Year Award. During that season, Vermes led Rutgers to their first victory in the NCAA Tournament in 26 years, scoring the winning goal in a contest against Seton Hall University.

Like many of the best American players, Vermes returned to the United States to join the recently founded MLS. In January 1995, he signed with the new league which would not begin league play until 1996. Therefore, MLS loaned Vermes to the New York Fever of the USISL where he played 25 games, scoring 16 goals in the 1995 season. In 1996, Vermes was drafted by the New York/New Jersey MetroStars in the third round of the MLS Inaugural Draft (29th overall) and captained the team in its first season. Although he played the most minutes of any MetroStar that year, the MetroStars traded Vermes on February 3, 1997 to the Colorado Rapids for Kerry Zavagnin. Vermes would play three years for the Rapids before being traded again, this time to the Kansas City Wizards with Matt McKeon for Scott Vermillion and a player allocation.

With the Wizards, Vermes had his best year in MLS in 2000, anchoring what may have been the best defense in MLS history. That Wizards team finished the season first in the league with a 16-7-9 record, having allowed only 29 goals in 32 games, and continued its defensive dominance in the playoffs, eventually winning the MLS Cup. Vermes was recognized as the MLS Defender of the Year, while his teammate Tony Meola won both the MLS Goalkeeper of the Year and MLS MVP awards. Vermes played two more seasons with the Wizards, struggling with injuries but playing every game he was healthy for, before announcing his retirement at the end of the 2002 season.

Vermes was never a star for the US national team, but he was a significant contributor for an extended period of time. Vermes received his first cap May 14, 1988 against Colombia, and would in all receive 67 caps for the team, playing in the 1988 Olympics, the 1990 World Cup and the 1991 CONCACAF Gold Cup. In the 1990 World Cup, he nearly bagged a goal against Italy with a scorching shot which Italian goalkeeper Walter Zenga barely stopped. A forward early in his career, his excellent performance in defense in MLS led to his comeback to the National team in that position after years of absence. He was the last player cut from the U.S. roster before the 1998 World Cup.

Vermes was appointed as the technical Director for the Kansas City Wizards of Major League Soccer on November 15, 2006. He was named interim manager of the Wizards on August 4, 2009, one day after predecessor Curt Onalfo was fired by the team. The team was in sixth place in MLS' Eastern Conference with a 5–6–7 record and coming off a 6–0 road loss to FC Dallas three nights earlier.[4] Vermes would lead to the Wizards to a 3-7-2 record down the stretch.

On November 9, 2009, it was reported that the Wizards would announce that they were removing the interim tag from his title.[5]

In additional to his work with the Wizards, Vermes worked as a broadcaster for the San Jose Earthquakes, serves as the technical Director of Coaching for the Blue Valley Soccer Club in Overland Park, Kansas, and was an assistant coach for the US Under-20 national team.